3.3 Properties of Logarithms
Feb 12­08:22
Change of Base Formula
Base 10: logax = log
log
Mar 2­12:27 PM
Change of Base Formula
10x
10a
Base e : logax =
-log 4 25
ln x
ln a
-log 4 25
Sep 19­10:14 AM
Sep 19­10:14 AM
Change of Base Formula
Base b : logax =
logbx
logba
-log 4 8
Sep 19­10:14 AM
Mar 2­12:39 PM
1
Properties of Logarithms
1. Loga(uv) = loga u + loga v
ln (uv) = ln u + ln v
-log
4
Properties of Logarithms
2. Log a
ln
8
u
v
u
v
= loga u - loga v
= ln u - ln v
- ln (2/27)
Sep 19­10:22 AM
Properties of Logarithms
3. Loga un = n loga u
ln un = n ln u
Sep 19­10:26 AM
Expand Logarithms
a) log45x3y
-log 2 (42 34)
2
b) logb x2
y z3
Sep 19­10:26 AM
Sep 19­10:33 AM
Condense Logarithms
a) 2 ln (x + 2) - ln x
b)
c)
Mar 2­12:53 PM
1
2 log10x
1
3
+ 3 log10 (x + 1)
[log2 x + log2 (x - 4)]
Sep 19­10:35 AM
2
Feb 27­7:29 AM
3